The biggest reason service caliber cartridges appear to not work very well is combat shot placement. Combat and hunting are two different environments. In combat shots are fired rapidly with rudimentary aiming a good deal of time, resulting in less than ideal shot placement. Hunting generally produces one well aimed shot.
In a defensive situation, the aggressor continuing to fight for several seconds or minutes after being shot is unacceptable. The same is not true in hunting. Even when shot by high power rifles deer can still run for a few seconds after being struck. The environments are totally different and comparing them is really apples to oranges.
At 20 yards, a well aimed shot from a .40 will dispatch a deer. That is contingent upon proper bullet selection. Arrows do it with 1/4 the kinetic energy. The wounding mechanism for an arrow and a pistol bullet are very similar. Cut and crush.